A zero determinant of the coefficient matrix doesn't necessarily imply that there are no solutions. If the rank of the coefficient matrix is smaller than the rank of the 'extended matrix' (coefficient matrix + column of constants) then you have a system without a solution.
However, it's possible that although the determinant of the coefficient matrix is zero, the system still has solutions. You will find an infinite number of solutions in that case, the equations were then linearly dependant.